Bottom Line:
However, the existence and salience of pitch also depends in a complex way on other factors, in particular harmonic content.For example, periodic sounds made of high-order harmonics tend to have a weaker pitch than those made of low-order harmonics.We also present a possible neural mechanism for pitch estimation based on coincidence detection, which does not require long delays, in contrast with standard temporal models of pitch.

ABSTRACTMusical notes can be ordered from low to high along a perceptual dimension called "pitch". A characteristic property of these sounds is their periodic waveform, and periodicity generally correlates with pitch. Thus, pitch is often described as the perceptual correlate of the periodicity of the sound's waveform. However, the existence and salience of pitch also depends in a complex way on other factors, in particular harmonic content. For example, periodic sounds made of high-order harmonics tend to have a weaker pitch than those made of low-order harmonics. Here we examine the theoretical proposition that pitch is the perceptual correlate of the regularity structure of the vibration pattern of the basilar membrane, across place and time-a generalization of the traditional view on pitch. While this proposition also attributes pitch to periodic sounds, we show that it predicts differences between resolved and unresolved harmonic complexes and a complex domain of existence of pitch, in agreement with psychophysical experiments. We also present a possible neural mechanism for pitch estimation based on coincidence detection, which does not require long delays, in contrast with standard temporal models of pitch.

f4: Neural network model of pitch estimation using within- and cross-channel structure. A, Spectrogram of a trumpet sound showing the first two harmonics. Two neurons with CF around the first harmonic and input delay δ receive the same signal (red and blue rectangles and input signals below). As a result, the two neurons fire synchronously for all three neuron models used: biophysical model of chopper and octopus cells, and leaky integrate-and-fire model (voltage traces). B, Spectrogram of a rolling sea wave sound, which shows no regularity structure. In particular, the two neurons do not receive the same signals (input, shaded area: difference between the two signals) and thus do not fire synchronously. C, Spectrogram of a harpsichord sound with unresolved harmonics in high frequency. The inset shows the periodicity of the envelope. Two neurons fire synchronously if they receive inputs from the same place delayed by δ = 1/f0. D, In the same high-frequency region, the inharmonic sound of a sea wave does not produce within-channel structure and therefore the two neurons do not fire synchronously. E, Synaptic connections for a pitch-selective group tuned to f0 = 220 Hz. Harmonics are shown on the left (red comb) superimposed on auditory filters. Resolved harmonics (bottom) produce regularity structure both across and within channels: color saturation represents the amplitude of the filter output while hue represents its phase for different delays (horizontal axis) and characteristic frequencies (vertical axis). Neurons with the same color fire synchronously and project to a common neuron. Unresolved harmonics (top) produce regularity structure within channels only. Here two identical colors correspond to two identical input signals only when the neurons have identical CF (same row). F, Same as E for f0 = 261 Hz, producing a different regularity structure, corresponding to a different synchrony pattern in input neurons. Synchronous neurons project to another group of neurons, selective for this pitch.

Mentions:
We tested different spiking neuron models (Fig. 4), defined by a membrane equation of the following form:(1)CdVdt=gLEL-V+yt+σξt+IV,where V is the membrane potential, gL(EL − V) represent the nonspecific leak current, σ is the noise level, C is the membrane capacitance and I(V) represents currents from voltage-gated channels.

f4: Neural network model of pitch estimation using within- and cross-channel structure. A, Spectrogram of a trumpet sound showing the first two harmonics. Two neurons with CF around the first harmonic and input delay δ receive the same signal (red and blue rectangles and input signals below). As a result, the two neurons fire synchronously for all three neuron models used: biophysical model of chopper and octopus cells, and leaky integrate-and-fire model (voltage traces). B, Spectrogram of a rolling sea wave sound, which shows no regularity structure. In particular, the two neurons do not receive the same signals (input, shaded area: difference between the two signals) and thus do not fire synchronously. C, Spectrogram of a harpsichord sound with unresolved harmonics in high frequency. The inset shows the periodicity of the envelope. Two neurons fire synchronously if they receive inputs from the same place delayed by δ = 1/f0. D, In the same high-frequency region, the inharmonic sound of a sea wave does not produce within-channel structure and therefore the two neurons do not fire synchronously. E, Synaptic connections for a pitch-selective group tuned to f0 = 220 Hz. Harmonics are shown on the left (red comb) superimposed on auditory filters. Resolved harmonics (bottom) produce regularity structure both across and within channels: color saturation represents the amplitude of the filter output while hue represents its phase for different delays (horizontal axis) and characteristic frequencies (vertical axis). Neurons with the same color fire synchronously and project to a common neuron. Unresolved harmonics (top) produce regularity structure within channels only. Here two identical colors correspond to two identical input signals only when the neurons have identical CF (same row). F, Same as E for f0 = 261 Hz, producing a different regularity structure, corresponding to a different synchrony pattern in input neurons. Synchronous neurons project to another group of neurons, selective for this pitch.

Mentions:
We tested different spiking neuron models (Fig. 4), defined by a membrane equation of the following form:(1)CdVdt=gLEL-V+yt+σξt+IV,where V is the membrane potential, gL(EL − V) represent the nonspecific leak current, σ is the noise level, C is the membrane capacitance and I(V) represents currents from voltage-gated channels.

Bottom Line:
However, the existence and salience of pitch also depends in a complex way on other factors, in particular harmonic content.For example, periodic sounds made of high-order harmonics tend to have a weaker pitch than those made of low-order harmonics.We also present a possible neural mechanism for pitch estimation based on coincidence detection, which does not require long delays, in contrast with standard temporal models of pitch.

ABSTRACTMusical notes can be ordered from low to high along a perceptual dimension called "pitch". A characteristic property of these sounds is their periodic waveform, and periodicity generally correlates with pitch. Thus, pitch is often described as the perceptual correlate of the periodicity of the sound's waveform. However, the existence and salience of pitch also depends in a complex way on other factors, in particular harmonic content. For example, periodic sounds made of high-order harmonics tend to have a weaker pitch than those made of low-order harmonics. Here we examine the theoretical proposition that pitch is the perceptual correlate of the regularity structure of the vibration pattern of the basilar membrane, across place and time-a generalization of the traditional view on pitch. While this proposition also attributes pitch to periodic sounds, we show that it predicts differences between resolved and unresolved harmonic complexes and a complex domain of existence of pitch, in agreement with psychophysical experiments. We also present a possible neural mechanism for pitch estimation based on coincidence detection, which does not require long delays, in contrast with standard temporal models of pitch.